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Search: id:A161599
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| A161599 |
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The list of the B values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2. |
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4
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| 1, 18, 305, 5167, 87534, 1482911, 25121953, 425590290, 7209912977, 122142930319, 2069219902446, 35054595411263, 593858902089025, 10060546740102162, 170435435679647729, 2887341859813909231, 48914376181156809198, 828657053219851847135, 14038255528556324592097
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The case C=15 of finding k such that C*k+1 and (C+4)*k+2 are both perfect squares (A160682).
The 2 equations are equivalent to the Pell equation x^2-285*y^2=1,
with x=(285*k+17)/2 and y=A*B/2.
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FORMULA
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B(t+2)=17*B(t+1)-B(t).
B(t)=((285+19*w)*((17+w)/2)^(t-1)+(285-19*w)*((17-w)/2)^(t-1))/570 where w=sqrt(285).
G.f.: (1+x)*x/(1-17*x+x^2).
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MAPLE
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t:=0: for b from 1 to 1000000 do a:=sqrt((15*b^2+4)/19):
if (trunc(a)=a) then t:=t+1: n:=(b^2-1)/19: print(t, a, b, n): end if: end do:
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PROGRAM
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(Other) sage: [(lucas_number2(n, 17, 1)-lucas_number2(n-1, 17, 1))/15 for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
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Cf. A160682, A161595 (sequence of A), A161583 (sequence of k).
Sequence in context: A167713 A166927 A113367 this_sequence A083451 A097831 A091045
Adjacent sequences: A161596 A161597 A161598 this_sequence A161600 A161601 A161602
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KEYWORD
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nonn,new
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AUTHOR
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Weisenhorn Paul (paulweisenhorn(AT)online.de), Jun 14 2009
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EXTENSIONS
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Edited, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2009
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